A mishmash of questions about lighting and messing with parallel line textures
#1 I think you got the general setup right, you use an Emission Shader node down to the Light Path node, but made a mistake in your setup. Down the nodetree you later mix the emission with a diffuse defeating the purpose. Also your node tree seems overly complicated, and unnecessarily convoluted for the setup.



#2 As Jerryno already mentioned, it is not trivial to do with material nodes alone, but see bellow.

#3 Add a Noise node to your texture coordinates, use a Color Mix node to control the amount of noise you add to the coordinates. Some scale change is to be expected, so compensate the size.



#4 Camera settings like Focal Length will dictate the perspective



Alternatively if you want true constant width, and don't mind a geometry based solution, convert your terrain to a mesh, select all the edges in one direction, and erase everything else. Convert it to a curve then use the Bevel Depth property to add constant thickness.